Maximum Entropy Estimation of n-Year Extreme Waveheights

A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)=αHγ e -βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α, β, and γ in the function are expressed in terms of the mean , variance V= (H-)2 and bias B= (H-)3 ; and (3) with , V and B estimated from observed data, the n -year return-period wave height H n is computed in accordance with the formula 11-F(H n)=n , where F(H n) is defined as F(H n)=∫ H n 0f(H) d H. Examples of estimating the 50 and 100-year return period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.